<< Chapter < Page Chapter >> Page >

The smallest data value is 60. Since the data with the most decimal places has one decimal (for instance, 61.5), we want our starting point to have two decimal places. Since the numbers 0.5, 0.05, 0.005, etc. are convenient numbers, use 0.05 and subtract it from 60, the smallest value, for the convenient starting point.

60 – 0.05 = 59.95 which is more precise than, say, 61.5 by one decimal place. The starting point is, then, 59.95.

The largest value is 74, so 74 + 0.05 = 74.05 is the ending value.

Next, calculate the width of each bar or class interval. To calculate this width, subtract the starting point from the ending value and divide by the number of bars (you must choose the number of bars you desire). Suppose you choose eight bars.

74.05 59.95 8 1.76

Note

We will round up to two and make each bar or class interval two units wide. Rounding up to two is one way to prevent a value from falling on a boundary. Rounding to the next number is often necessary even if it goes against the standard rules of rounding. For this example, using 1.76 as the width would also work. A guideline that is followed by some for the width of a bar or class interval is to take the square root of the number of data values and then round to the nearest whole number, if necessary. For example, if there are 150 values of data, take the square root of 150 and round to 12 bars or intervals.

The boundaries are:

  • 59.95
  • 59.95 + 2 = 61.95
  • 61.95 + 2 = 63.95
  • 63.95 + 2 = 65.95
  • 65.95 + 2 = 67.95
  • 67.95 + 2 = 69.95
  • 69.95 + 2 = 71.95
  • 71.95 + 2 = 73.95
  • 73.95 + 2 = 75.95

The heights 60 through 61.5 inches are in the interval 59.95–61.95. The heights that are 63.5 are in the interval 61.95–63.95. The heights that are 64 through 64.5 are in the interval 63.95–65.95. The heights 66 through 67.5 are in the interval 65.95–67.95. The heights 68 through 69.5 are in the interval 67.95–69.95. The heights 70 through 71 are in the interval 69.95–71.95. The heights 72 through 73.5 are in the interval 71.95–73.95. The height 74 is in the interval 73.95–75.95.

The following histogram displays the heights on the x -axis and relative frequency on the y -axis.

Histogram consists of 8 bars with the y-axis in increments of 0.05 from 0-0.4 and the x-axis in intervals of 2 from 59.95-75.95.

Try it

The following data are the shoe sizes of 50 male students. The sizes are continuous data since shoe size is measured. Construct a histogram and calculate the width of each bar or class interval. Suppose you choose six bars.
9; 9; 9.5; 9.5; 10; 10; 10; 10; 10; 10; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5
11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11.5; 11.5; 11.5; 11.5; 11.5; 11.5; 11.5
12; 12; 12; 12; 12; 12; 12; 12.5; 12.5; 12.5; 12.5; 14

Smallest value: 9

Largest value: 14

Convenient starting value: 9 – 0.05 = 8.95

Convenient ending value: 14 + 0.05 = 14.05

14.05 8.95 6 = 0.85

The calculations suggests using 0.85 as the width of each bar or class interval. You can also use an interval with a width equal to one.

Got questions? Get instant answers now!

The following data are the number of books bought by 50 part-time college students at ABC College. The number of books is discrete data , since books are counted.
1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1
2; 2; 2; 2; 2; 2; 2; 2; 2; 2
3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3; 3
4; 4; 4; 4; 4; 4
5; 5; 5; 5; 5
6; 6

Eleven students buy one book. Ten students buy two books. Sixteen students buy three books. Six students buy four books. Five students buy five books. Two students buy six books.

Because the data are integers, subtract 0.5 from 1, the smallest data value and add 0.5 to 6, the largest data value. Then the starting point is 0.5 and the ending value is 6.5.

Next, calculate the width of each bar or class interval. If the data are discrete and there are not too many different values, a width that places the data values in the middle of the bar or class interval is the most convenient. Since the data consist of the numbers 1, 2, 3, 4, 5, 6, and the starting point is 0.5, a width of one places the 1 in the middle of the interval from 0.5 to 1.5, the 2 in the middle of the interval from 1.5 to 2.5, the 3 in the middle of the interval from 2.5 to 3.5, the 4 in the middle of the interval from _______ to _______, the 5 in the middle of the interval from _______ to _______, and the _______ in the middle of the interval from _______ to _______ .

  • 3.5 to 4.5
  • 4.5 to 5.5
  • 6
  • 5.5 to 6.5
Got questions? Get instant answers now!

Calculate the number of bars as follows:

6.5 0.5 number of bars 1

where 1 is the width of a bar. Therefore, bars = 6.

The following histogram displays the number of books on the x -axis and the frequency on the y -axis.

Histogram consists of 6 bars with the y-axis in increments of 2 from 0-16 and the x-axis in intervals of 1 from 0.5-6.5.
Got questions? Get instant answers now!

Questions & Answers

a survey of a random sample of 300 grocery shoppers in Kimberly mean value of their grocery was R78 proportion standard deviation of grocery purchase value is R21 the 95% confidence interval mean grocery purchase
sindisiwe Reply
We're would I find; The Z score?
Michael Reply
in your text at the back
Vincent
A student is known to answer 3 questions out of 5 and another student 5 out of 7. if a problem is given to both of them assuming independent work. find the probability none of them will solve it.
Mitiku Reply
Cumulative usersLine quality Throughput and Ping Cumulative transfers Logging policySSL-VPN Windows (comfortable)L2TP/IPsec Windows, Mac, iPhone, Android No client requiredOpenVPN Windows, Mac, iPhone, AndroidMS-SSTP Windows Vista, 7, 8, RT No client requiredVolunteer operator's name (+ Operator's m
Mitiku
Population of children in one word
mmaphuthego Reply
It has been claimed that less than 60% of all purchases of a certain kind of computer program will call the manufacturer’s hotline within one month purchase. If 55 out 100 software purchasers selected at random call the hotline within a month of purchase, test the claim at 0.05 level of significance
Mharfe Reply
what is the parameter of the hypotesis (Ho: u=75) (HA:u=/75)
Kristine Reply
how can I understand the concept of set and set operation
Monday
multiple correlation coefficient is denoted by
Alamdar Reply
how prepare satistic when remaining only two days inn examinatin
Sonia
how to find product moment correlation cofficient
zaib Reply
A research study wishes to examine the proportion of hypertensive individuals among three different groups of exercises: marathon runners, yoga, and CrossFit. Of the 78 marathon runners, 14 are hypertensive. Of the 63 yoga practioners, 6 are hypertensive. And there are 16 hypertensive subjects among the 54 CrossFit athletes What type of test statistic do you need to run for this type of analysis?
zainab Reply
A research study wishes to examine the proportion of hypertensive individuals among three different groups of exercises: marathon runners, yoga, and CrossFit. Of the 78 marathon runners, 14 are hypertensive. Of the 63 yoga practioners, 6 are hypertensive. And there are 16 hypertensive subjects among the 54 CrossFit athletes What type of test statistic do you need to run for this type of analysis? plz solve this
zainab
2. The data that categories patients as males or females are known
shivani Reply
categorical data
Sneha
hi
Mitiku
20 25 find the area under the normal curve
Akram Reply
find the area normal curve
Akram
Let x1, x2, ...,xn be a random sample of size n from N(0,σ  ), show that there exists an UMP test with significance level α for testing H0 :  2 =  2 against H1 :  2 <  2 . If n=15,  = 0.05, and  2= 3, determine the BCR
Bhavana Reply
explain null and alternative hypothesis are formulated
Shams
please give me reply quickly
Shams
3xy^2√[x^3y^2/(12(x^3y)^2)]
Esther Reply
what is probability
Esther
what is probability
Esther
what is probability
Esther
Probability is a branch of mathematics that deals with the occurrence of a random event. For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.
Dewan
explain null and alternative hypothesis are farmulated
Shams
please give answer quickly
Shams
quick
Shams
mean 0 and standard deviation 1 .using area table find P(X>3)
Naeem Reply
hi
Shams
what is terms data?
Mohsin Reply
define the types of data?
Mohsin
define the number of classes?
Mohsin
define the class limt?
Mohsin
define the class frequency and class interval ?
Mohsin
define class boundaries
George
Your home address nominal Interval ratio ordinal
MD
home address is nominal
Awel

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask